From the relation `R=R_0A^(1/3)`, where `R_0`is a constant and A is the mass number of a nucleus , show that the nuclear matter density is nearly constant.(i.e., independent of A)

Show that 1-2sinthetacosthetage0 for all theta in R

At constant volume, the specific heat of a gas is (3R)/2 , then the value of ' gamma ' will be

A spherically symmetric gravitational system of particles has a mass density rho={(rho_0,for, r,lt,R),(0,for,r,gt,R):} where rho_0 is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed v as a function of distahce r(0ltrltOO) form the centre of the system is represented by

For a gas R/C_V = 0.4, where R is the universal gas constant and C, is molar specific heat at constant volume. The gas is made up of molecules which are

The centr of mass of a right circular coneof height h, radius R and constant density rho is at

The differential equation of the family of curves v=A/r+B , where A and B are arbitrary constants, is

Kepler's third law states that square of period revolution (T) of a planet around the sun is proportional to third power of average distance i between sun and planet i.e. T^(2)=Kr^(3) here K is constant if the mass of sun and planet are M and m respectively then as per Newton's law of gravitational the force of alteaction between them is F=(GMm)/(r^(2)) , here G is gravitational constant. The relation between G and K is described as

Show that the escape velocity of a body from the surface of a planet of radius R and mean density rho is Rfrac(sqrt8pirhoG)(3) OR Show that the escape velocity of a body from the surface of the earth is 2Rfrac(sqrt2pirhoG)(3) , where R is the radius of the earth and rho is the mean density of the earth. OR Obtain formula of escape velocity of a body at rest on the earth's surface in terms of mean density of erth.

The wave number of first line in Balmer series of hydrogen spectrum is (Rydberg constant, R_H = 109,678 cm^-1 ) nearly

The angular velocity of rotation of star (of mass M and radius R ) at which the matter start to escape from its equator will be